Polynomial hulls of arcs and curves
Polynomial hulls of arcs and curves
复制标题
DOI：
10.1090/proc/15138
复制
发表时间：
2019-12
影响因子：
1
通讯作者：
Alexander J. Izzo
中科院分区：
文献类型：
--
作者：
Alexander J. Izzo
证明了C3\mathbb {C}^3中存在弧和简单闭曲线，其非平凡多项式壳不含解析圆.证明了在C N \mathbb {C}^N（N ≥ 2 N \geq 2）中，任何有界连通的全纯Runge域都存在多项式凸弧和几乎满测度的简单闭曲线.这些结果，加强早先的结果，作者，得到的后果多项式外壳的圆弧和简单的封闭曲线通过紧凑，完全不连通集的一般结果。
It is shown that there exist arcs and simple closed curves in C 3 \mathbb {C}^3 with nontrivial polynomial hulls that contain no analytic discs. It is also shown that in any bounded, connected Runge domain of holomorphy in C N \mathbb {C}^N ( N ≥ 2 N \geq 2 ) there exist polynomially convex arcs and simple closed curves of almost full measure. These results, which strengthen earlier results of the author, are obtained as consequences of a general result about polynomial hulls of arcs and simple closed curves through compact, totally disconnected sets.